The Standard Model has enjoyed considerable success in describing a whole range of phenomena in particle physics. However, the model is considered incomplete because it provides little understanding of other empirical observations such as, the existence of three generations of leptons and quarks, which apart from mass have similar properties. This paper examines in some detail the basic assumptions upon which the Standard Model is built and compares these with the assumptions of an alternative model, the Generation Model. The Generation Model provides agreement with the Standard Model for those phenomena which the Standard Model is able to describe, but it is shown that the assumptions inherent in the Generation Model allow progress beyond the Standard Model.
The Standard Model (SM) of particle physics [
The SM has enjoyed considerable success in describing the interactions of leptons and the multitude of hadrons (baryons and mesons) with each other as well as the decay modes of the unstable leptons and hadrons. However, the model is considered to be incomplete in the sense that it provides little understanding of several empirical observations such as the existence of three families or generations of leptons and quarks, which apart from mass have similar properties; the mass hierarchy of the elementary particles, which form the basis of the SM; the nature of the gravitational interaction, and the origin of
The inability of the SM to provide an understanding of such important empirical observations has become very frustrating to particle physicists, especially the experimentalists, who find that all their other data are adequately described by the SM. In order to comprehend this dilemma and to progress beyond the SM, it is timely to reconsider the basic assumptions upon which the SM is built.
An excellent analogy of the SM situation [
Progress in understanding the universe was only made when the Ptolemaic model was replaced by the CopernicanKeplerian model, in which the Earth moved like the other planets around the Sun, and Newton discovered his universal law of gravitation to describe the approximately elliptical planetary orbits. Indeed, it was only by removing the incorrect assumption that celestial bodies moved in “divine circles” that progress beyond the Ptolemaic model was achieved.
During the last decade, an alternative model to the SM, the Generation Model (GM), has been developed [
There are three essential differences between the GM and the SM: (a) the classification of the leptons and quarks in terms of additive quantum numbers, (b) the roles played by the mass eigenstate quarks and the weak eigenstate quarks, and (c) the nature of the weak interactions. Each of these essential differences will be examined in the following three subsections.
In the SM, the elementary particles that are the constituents of matter are assumed [
In the SM, the leptons and quarks are allotted several additive quantum numbers. Table
SM additive quantum numbers for leptons.
Particle 






0  1  0  0 

−1  1  0  0 

0  1  1  0 

−1  1  1  0 

0  1  0  1 

−1  1  0  1 
SM additive quantum numbers for quarks.
Particle 








+2/3  1/3  0  0  0  0 

−1/3  1/3  0  0  0  0 

+2/3  1/3  0  1  0  0 

−1/3  1/3  −1  0  0  0 

+2/3  1/3  0  0  0  1 

−1/3  1/3  0  0  −1  0 
Tables
The additive quantum numbers
The introduction of the above additive quantum numbers to both leptons and quarks took place over a considerable period of the 20th century in order to account for the observed interactions of the leptons and the multitude of hadrons (baryons and mesons) as well as the decay modes of the unstable leptons and hadrons.
The additive quantum numbers allotted to leptons (Table
Similarly, in general, the additive quantum numbers allotted to quarks (Table
Later in 1953, the strangeness quantum number was introduced to resolve the paradox of the copious associated production of strange particles and their individual very slow decay modes. Although strangeness was assumed to be conserved in strong interactions so that the strange particles were produced in pairs, strangeness was required to change by one unit as the individual strange particles slowly decayed. The nonconservation of strangeness by one unit in weak interaction processes suggested that this additive quantum number arose from some approximate, rather than an exact symmetry, in nature.
As more particles were discovered, the remaining additive quantum numbers,
An important property of the weak interactions discovered in the late 1940s was their “universality”. Analysis of experiments revealed that the coupling constants for muon decay and muon capture were of the same order of magnitude as those for
To summarize, the SM classification of leptons and quarks in terms of the additive quantum numbers displayed in Tables
In the GM, all the above problems are overcome by the adoption of a
GM additive quantum numbers for leptons and quarks.
Particle 



Particle 





0  −1  0 

+2/3  1/3  0 

−1  −1  0 

−1/3  1/3  0 

0  −1  ±1 

+2/3  1/3  ±1 

−1  −1  ±1 

−1/3  1/3  ±1 

0  −1  0, ±2 

+2/3  1/3  0, ±2 

−1  −1  0, ±2 

−1/3  1/3  0, ±2 
Another feature of the GM classification scheme is that all three additive quantum numbers
Comparison of Tables
The development of the GM classification scheme (Table
It should be noted that the development of a composite GM is not possible in terms of the nonunified classification scheme of the SM, involving different additive quantum numbers for leptons than for quarks and the nonconservation of some additive quantum numbers, such as strangeness, in the case of quarks.
Composite versions of the GM have been developed during the last decade [
The starting point for the development of the CGM was the very similar schematic models of Harari [
The CGM represents a major extension of the HarariShupe model with the introduction of a third kind of rishon, the
CGM additive quantum numbers for rishons.
Rishon 





+1/3  +1/3  0 

0  +1/3  0 

0  +1/3  −1 
It is assumed that each kind of rishon carries a color charge, red, green, or blue, while their antiparticles carry an anticolor charge, antired, antigreen, or antiblue. The CGM postulates a strong colortype interaction corresponding to a local gauge
In the CGM, each lepton of the first generation (Table
CGM of first generation of leptons and quarks.
Particle  Structure 






+1  +1  0 


+2/3  +1/3  0 


+1/3  −1/3  0 


0  −1  0 


0  +1  0 


−1/3  +1/3  0 


−2/3  −1/3  0 


−1  −1  0 
In the CGM, it is assumed that each quark of the first generation is a composite of a colored rishon and a colorless rishonantirishon pair,
The rishon structures of the second generation particles are assumed to be the same as the corresponding particles of the first generation plus the addition of a colorless rishonantirishon pair,
Similarly, the rishon structures of the third generation particles are assumed to be the same as the corresponding particles of the first generation plus the addition of two
The color structures of both second and third generation leptons and quarks have been chosen so that the CC weak interactions are universal. In each case, the additional colorless rishonantirishon pairs,
In the CGM, the three independent additive quantum numbers, charge
To summarize, the GM provides both a
The GM is obtained from the SM essentially by interchanging the roles of the mass eigenstate quarks and the weak eigenstate quarks [
In the SM, the observed universality of the CC weak interactions in the lepton sector is described by assuming that each mass eigenstate charged lepton forms a weak isospin doublet (
Thus, for leptonic processes, the concept of a universal CC weak interaction allows one to write (for simplicity we restrict the discussion to the first two generations only)
On the other hand, the universality of the CC weak interactions in the quark sector is treated differently in the SM. For simplicity, we again restrict the discussion to the first two generations of quarks although the extension of the discussion to all three generations involves no essential changes. In the SM, it is assumed that the up
In terms of transition amplitudes, (
In hindsight, the above technique for accommodating the universality of the CC weak interactions in the quark sector arose from two assumptions: firstly, the introduction of the strangeness quantum number
Thus, to summarize, the significant dubious assumption involved in the SM’s method of accommodating the universality of the CC weak interactions in the quark sector is that the
The GM overcomes the above problem inherent in the SM by postulating two different assumptions.
Firstly, the GM postulates that the mass eigenstate quarks of the same generation, that is,
Secondly, the GM postulates that hadrons are composed of weak eigenstate quarks such as
The GM differs from the SM in that it treats quark mixing differently from the method introduced by Cabibbo [
The SM recognizes [
For consistency, one theoretical requirement of a local gauge field mediated by vector (spin1) particles is that these “gauge bosons” should be
The charged nature of the weak interaction gauge bosons means that the symmetries of the weak and electromagnetic interactions become entwined. In the SM, it is assumed, following a proposal by Glashow [
This “electroweak theory” was a major step towards understanding the socalled “electroweak connection”:
For the extended symmetry,
In the SM, these inconsistency problems are all overcome by postulating the existence of a condensate, analogous to the condensate of Cooper pairs in the microscopic theory of superconductivity, called the Higgs field. This new field is assumed to be a ubiquitous energy field so that it exists throughout the entire universe. It is accompanied by a new fundamental particle called the Higgs boson, which continuously interacts with other elementary particles by transferring energy from the Higgs field so that these particles acquire mass. This process is called the Higgs mechanism [
The boson mass problem was resolved by Weinberg [
A second theoretical requirement of a local gauge theory involving spin1 mediating particles is that it should be “renormalizable”, that is, that any infinities arising in any calculated quantities should be capable of being made finite by acceptable renormalization techniques. In 1971, ’t Hooft showed [
However, in spite of these successes, the electroweak theory still has several problems. Firstly, it requires the existence of a new massive spin0 boson, the Higgs boson, which notwithstanding some recent tantalizing results from the LHC [
The electroweak theory of the SM also has a few unanswered questions concerning its structure: How does the symmetry breaking mechanism occur within the electroweak interaction? What is the principle which determines the large range of fermion masses exhibited by the leptons and quarks?
The GM adopts [
Thus, in the GM, the weak interactions are assumed to be “effective” interactions; that is, they are approximate interactions that contain the appropriate degrees of freedom to describe the experimental data occurring at sufficiently low energies for which any substructure and its associated degrees of freedom may be ignored. In the GM [
The nonfundamental nature of the weak interactions in the GM means that the question of renormalizability does not arise. Thus, the mediating particles may be massive since this does not destroy any
The GM represents progress beyond the SM, providing understanding of several empirical observations, which the SM is unable to address: (i) the existence of three generations of leptons and quarks, which apart from mass have similar properties; (ii) the mass hierarchy of the elementary particles, which form the basis of the SM; (iii) the nature of the gravitational interaction, and (iv) the origin of
Progress beyond the SM was largely achieved by the development of the much
The unified classification scheme of the GM indicated that leptons and quarks are intimately related and led to the development of composite versions of the GM, which we refer to as the Composite Generation Model (CGM) [
In addition the CGM led to a new paradigm for the origin of
In the CGM, the elementary particles of the SM have a substructure, consisting of massless rishons and/or antirishons bound together by strong color interactions, mediated by massless neutral hypergluons. This model is very similar to that of the SM in which quarks and/or antiquarks are bound together by strong color interactions, mediated by massless neutral gluons, to form hadrons. Since the mass of a hadron arises mainly from the energy of its constituents, the CGM suggests [
The CGM suggests that the mass hierarchy of the three generations arises from the substructures of the leptons and quarks [
In the CGM, it is envisaged that the rishons and/or antirishons of each lepton or quark are very strongly localized, since to date there is no direct evidence for any substructure of these particles. Thus the constituents are expected to be distributed according to quantum mechanical wave functions for which the product wave function is significant for only an
The mass of each lepton or quark corresponds to a characteristic energy primarily associated with these intrafermion color interactions. It is expected that the mass of a composite particle will be greater if the degree of localization of its constituents is smaller (i.e., the constituents that are on average more widely separated). This is a consequence of the nature of the strong color interactions, which are assumed to possess the property of “asymptotic freedom” [
In the CGM [
Each lepton of the second and third generations is envisaged to be similar to the corresponding lepton of the first generation with one and two additional colorless rishonantirishon pairs, respectively, being attached externally to the triangular distribution, leading quantum mechanically to a less localized distribution of the constituent rishons and antirishons so that the leptons of the second and third generations have increasing significantly larger masses than its corresponding first generation lepton.
In the CGM each quark of the first generation is a composite of a colored rishon and a colorless rishonantirishon pair. This color charge structure of the quarks is expected to lead to a quantum mechanical
Each quark of the second and third generations has a similar structure to that of the corresponding quark of the first generation, with one and two additional colorless rishonantirishon pairs, respectively, being attached quantum mechanically so that the whole rishon structure is a longer linear distribution of the constituents. These structures are considerably less localized leading to increasing significantly larger masses than the corresponding first generation quark.
The
To summarize, the mass hierarchy of the three generations of leptons and quarks is described by the degree of localization of their constituent rishons and/or antirishons. The degree of localization depends very sensitively upon both the color charge and the electric charge structures of the composite particle.
In the CGM, between any two leptons and/or quarks there exists a residual interaction arising from the color interactions acting between the constituents of one fermion and the constituents of the other fermion. We refer to these interactions as
The mass of a body of ordinary matter is essentially the total mass of its constituent electrons, neutrons, and protons. In the CGM, each of these three particles is considered to be colorless. The electron is composed of three charged antirishons, each carrying a different anticolor charge, antired, antigreen, or antiblue. Both the neutron and the proton are composed of three quarks, each carrying a different color charge, red, green, or blue. All three particles are assumed to be essentially in a threecolor antisymmetric state, so that their behavior with respect to the strong color interactions is expected basically to be the same. This similar behavior suggests that the interfermion interactions of the CGM between electrons, neutrons, and protons have several properties associated with the usual gravitational interaction [
In the CGM, the above interfermion color interactions suggest a universal law of gravitation, which closely resembles Newton’s original law that a body of mass
This difference arises from the selfinteractions of the hypergluons mediating the interfermion color interactions [
This change in the gravitational interaction, especially for large separations of the interacting masses, has been shown [
As discussed in Section
In the CGM, the constituents of quarks are rishons and antirishons. If one assumes the simple convention that all rishons have positive parity and all their antiparticles have negative parity, one finds that the down and strange quarks have opposite intrinsic parities, according to the proposed structures of these quarks in the CGM [
In the SM, the intrinsic parity of the charged pions is assumed to be
Morrison and Robson [
In the CGM, the
Although the SM has enjoyed considerable success in describing the interactions of leptons and hadrons with each other as well as their decay modes, the model is considered to be incomplete in that it provides little understanding of several empirical observations such as the existence of three generations of leptons and quarks, which apart from mass have similar properties. Consequently, we have closely examined the basic assumptions upon which the SM is erected.
It has been found that the SM is founded upon three dubious assumptions, which present major stumbling blocks preventing progress beyond the SM. These are (i) the assumption of a diverse complicated scheme of additive quantum numbers to classify its elementary particles, (ii) the assumption of weak isospin doublets in the quark sector to accommodate the universality of the CC weak interactions and (iii) the assumption that the weak interactions are fundamental interactions described by a local gauge theory.
The SM diverse complicated classification scheme of leptons and quarks is nonunified in the sense that leptons and quarks are allotted different kinds of additive quantum numbers, preventing any possibility of developing a model describing any substructure of these particles. Although no such substructure has been detected to date, there are several empirical observations (e.g., the electron and the proton have exactly opposite electrical charges, the three generations of leptons and quarks, etc.), which suggest that both leptons and quarks probably do have a substructure. In addition, the SM fails to provide any physical basis for its adopted classification scheme.
The assumption of weak isospin doublets
The assumption that the weak interactions are fundamental interactions arising from a local gauge theory is at variance with the experimental facts: both the
However, the resultant electroweak theory still has many problems and leaves several questions unanswered: How does the symmetry breaking mechanism occur within the electroweak theory? What is the principle which determines the large range of fermion masses exhibited by the leptons and quarks?
In the GM, the three dubious assumptions of the SM discussed above are replaced by three different and simpler assumptions. These are (i) the assumption of a simpler and unified classification of leptons and quarks; (ii) the assumption that the mass eigenstate quarks form weak isospin doublets and that hadrons are composed of weak eigenstate quarks; and (iii) the assumption that the weak interactions are not fundamental interactions.
In the GM, both the leptons and quarks are classified in terms of only three additive quantum numbers: charge
The GM treats quark mixing differently from the method introduced by Cabibbo and employed in the SM. The GM postulates that the mass eigenstate quarks form weak isospin doublets and couple with the full strength of the CC weak interaction, while hadrons are composed of weak eigenstate quarks such as
The GM assumes that the weak interactions are not fundamental interactions arising from a local gauge theory but rather are residual interactions of the strong color interactions, responsible for binding the constituents of the leptons and quarks together. Thus, in the GM, the weak interactions are assumed to be “effective” interactions and the massive vector bosons, which mediate the effective weak interactions, are analogous to the massive mesons, which mediate effective nuclear interactions between nucleons.
The three alternative assumptions of the GM, discussed above, allow progress beyond the SM.
Firstly, the unified classification scheme of the GM led to the development of composite versions of the GM; that is, the elementary particles of the SM have a substructure, consisting of massless rishons and/or antirishons bound together by strong color interactions, mediated by massless neutral hypergluons. Since the mass of a hadron arises mainly from the energy of its constituents, the CGM suggested that the mass of a lepton, quark, or vector boson arises entirely from the energy stored in the motion of its constituent rishons and/or antirishons and the energy of the color hypergluon fields. In addition it indicated that if a particle has mass, then it is composite. Thus, unlike the SM, the GM provides a unified description of
Secondly, the CGM suggested that the large variation (<3 eV to 175 GeV) in the masses of the leptons and quarks may be described by the degree of localization of their constituent rishons and/or antirishons, the degree of localization depending very sensitively upon both the color charge, and the electric charge structure of the composite particle. In addition, the CGM predicts that the
Thirdly, the similar behavior of the interfermion color interactions of the CGM between electrons, neutrons, and protons, the constituents of ordinary matter, suggests that these residual color interactions may be identified with the usual gravitational interaction. Indeed, in the CGM, the interfermion color interactions suggest a universal law of gravitation, which is very similar to Newton’s original law but with one significant difference: the usual constant of gravitation
Fourthly, the GM assumes that hadrons are composed of weak eigenstate quarks, that is, mixedquark states. This gives rise to several important consequences, which differ from the predictions of the SM: (i) the CGM predicts [
In addition, the mixedquark states can have mixed parity. For the CGM, it is found that the
Apparent
Thus, it is timely to embrace the GM as a refinement of the SM and to employ both the GM and the CGM to further progress beyond the SM.
The author is grateful to N. H. Fletcher, D. Robson, and J. M. Robson for helpful discussions.